Tuesday, December 2, 2014

How Gravity continuously does Work on the atmosphere to control pressure & temperature

Some commenters claim gravity is not continuously performing thermodynamic Work upon the atmosphere to generate the thermal gradient from the continuous compression/expansion of gas parcels or packets continuously moving up and down within the lower atmosphere. This is the source of the 33C gravito-thermal greenhouse effect, so we will now demonstrate why this misconception is incorrect by using the 1st Law of Thermodynamics (law of conservation of energy), ideal gas law, and barometric formulae.
Beginning with the 1st Law of Thermodynamics:

where

is change in internal energy

and are quantities of heat supplied to the system by its surroundings and of work done by the system on its surroundings, respectively.

When a system expands [e.g. the inflation of the atmosphere by solar radiative forcing] in a fictive quasistatic process, the work done by the system on the environment is the product, +P dV, of pressure, P, and volume change, dV, whereas the work done on the system is -P dV. Using either sign convention for work, the change in internal energy of the system is:

The two sides of the 1st law equation must balance with change in internal energy for the atmosphere ~0. Note the Work done on the right side of the equation is the work done by gravitational forcing on the atmosphere = F = ma = mg for the atmosphere by the continuous compression of cold, descending air packets and the gravitational potential energy PE that convecting warm air packets accumulate as they rise, expand, and cool. In the 1st law above, the Work done on the right side is from the expansion/compression of air packets continuously rising and falling in the atmosphere ad infinitum. This continuous compression by gravity of cold gas packets descending adiabatically from the upper atmosphere down to the surface is what is continuously doing Work (W = pda = Pressure*change in specific volume (a)) upon the atmosphere. By the ideal gas law, this continuous work or compression of gas packets increases their pressure as they descend toward the surface, thus creating the temperature gradient within the troposphere.Also note, greenhouse gases are passive IR absorbers/emitters and not a source of any heat energy on the left side of the equation.

Note "changes in temperature result from either expansion or contraction" and "adiabatic processes play a large role in deep convective processes"

The Poisson Relation as the entire source of the atmospheric temperature gradient (gravito-thermal greenhouse effect), not radiative forcing from greenhouse gases, was perhaps first described by the great physicist Maxwell. These same barometric relations are the basis of all the barometric formulae and the greenhouse equation.

Thus, gravity is continuously doing the work upon air packets/parcels ascending (which are accumulating gravitational potential energy) and air packets/parcels descending (which in the process are using up their gravitational potential energy in exchange for the work done by gravity on continuous compression of air packets/parcels).

This demonstrates how gravity creates the thermal gradient above and below the equilibrium temperature with the Sun, while conserving energy:

Equilibrium temperature with the Sun = 255K

Ts = temperature at Earth's surface = 288K

Tt = temperature at the tropopause = 220K at around 15,000 km height

"Average temperature" of the quasi-linear [lapse rate] temperature gradient of the troposphere:

Note the units of pressure used in the greenhouse equation are in unit atmospheres, and by definition 1 atmosphere of pressure at the surface = 1.01325×105 Newtons/meter squared, which is the continuous gravitational forcing F = mg upon the atmosphere by gravity which is producing the gravito-thermal greenhouse effect. Newton's 2nd law of motion F = ma = mg appears in the greenhouse equation as annotated below to calculate this gravitational forcing upon the atmospheric mass:

35 comments:

Note that during the very first convective cycle, whilst KE (equivalent to 33K) is being converted to PE and no PE is yet being returned to the near surface, the surface is losing energy by radiation to space AND to the first convective cycle via conduction.so the surface temperature will drop below 255K for a while.

When the first convective cycle completes and adiabatically warmed air is being returned to the surface at the same rate as surface warmth is being taken up adiabatically then the surface temperature rises to 288K because:

i) Incoming solar energy continues to arrive at a rate commensurate with a surface temperature of 255K AND

ii) Descending adiabatically warmed air is returning to the surface at a rate commensurate with surface warming of 33K AND

iii) The next convective cycle is simultaneously removing KE from the surface at a rate commensurate with surface warming of 33K thereby locking it away in PE which is not heat and does not radiate.

The net outcome is that the surface temperature of 288K is provided by 255K from the sun plus 33K from descending air but the surface cannot use that 33K for radiation to space because it is recycled into further convective uplift. Nevertheless the surface temperature will still be enhanced by 33K because the energy required by the ongoing convective cycle is still held at the surface.

The result is a surface temperature of 288K, 255K escaping via radiation to space and 33K continuing to support the weight of the atmosphere.

Some AGW proponents say that adiabatically descending air that has been warmed cannot heat the surface.

It doesn't have to warm the surface directly. All it has to do is provide a less steep lapse rate which inhibits convection so that the surface warms from solar irradiation more than it otherwise would have done.

We see that all the time within atmospheric high pressure cells containing descending air and often they create an inversion which blocks convection altogether.

The irony is that reducing or blocking convection is what the glass in greenhouses does.

That descending adiabatically warmed air acts just like the glass on a greenhouse roof by reducing convection so it is mass acting via the adiabatic convective overturning cycle that is and always was the true greenhouse effect.

Yes good points, thanks again Stephen for your assistance on debunking the myths about the gravito-thermal GHE.

I'm doing a round-up post now of all the myths/strawmen about the gravito-thermal GHE and linking to a debunking of each myth, so let me know what are the most common strawman arguments you've heard and a link to a comment or post debunking that particular myth so I can gather convenient links to all of the debunkings on one page. That way we won't have to keep repeating ourselves ad nauseum and can just post one link to that page. Sound good?

Please leave as a comment on this post anything you wish to provide. Thanks

The term 'Greenhouse Effect' must have been originally coined by a meteorologist maybe 100 years or more ago who realised that adiabatically warmed air by virtue of being transparent and inhibiting convection would act exactly like a greenhouse roof.

The radiative chaps never learned that so they often say that the term is misleading.

The term might be misleading in terms of their attempt to use it in connection with their imagined radiative only scenario but it is spot on in terms of long established meteorology.

The thing is that meteorology was a very arcane subject in the 20th century and earlier.

Hardly anyone knew anything about it and a lot of the ways the laws of physics play out within an actual atmosphere are counterintuitive and hard to envisage such as the thorny concept of adiabatic processes.Everyone I discuss it with is oblivious to its true nature.

In the 1980s or thereabouts a bunch of astrophysicists thought they could take over climate science with no knowledge of basic meteorolgy and they have spread nothing but confusion in their wake.

Made them rich and famous though.

The Greenhouse Effect is perfectly described as a process that occurs as a result of a transparent layer of warm air that inhibits convection so as to allow the sun to warm the surface to above the S-B figure of 255K.

On average for the Earth as a whole the surface temperature enhancement for the mass induced ghreenhouse effect is 33K leaving no room for any contribution from radiative gases.

Maxwell had it most of it figured out with the Poisson relation way back in 1872, but nobody paid much attention unfortunately. Twenty six years later after Maxwell was long dead, Arrhenius came up with his radiative theory which completely ignores convection, falsely blaming the gravito-thermal GHE on CO2 radiative forcing instead. Arrhenius' convection-ignoring theory falsified by RW Wood in 1909 and many others since.

Do you have any references, books, papers etc from that period in the 1950-1960's to share regarding the gravito-thermal GHE? Or calculate the entire temperature profile without any GHG "radiative forcing"

Bear in mind that since atmospheric mass is a constant the mass induced greenhouse effect was then taken as a given that required no discussion.

Only when the radiative theory came to the fore was there any question that the greenhouse effect might be variable.

The Standard Atmosphere dates from before the 50s and 60s and of course there are the Gas Laws and neither of them contains any term or variable parameter relating to radiative characteristics of atmospheric gases.

If anyone had been listening to Arrhenius they would have done, don't you think ?

He was basically ignored until he became 'useful.'They both rely entirely on mass and gravity plus insolation.

A rising parcel of air loses internal energy and converts an increasing proportion of it from kinetic to potential energy.

Now what you are saying is fairly plausible but what you must ask yourself ‘does it correspond to reality?’

Theres an easy way to find out.

Your theory is the loss of internal energy on ascent is turned into potential energy.

Lets work through a problem where we are all agreed about the numbers used

So take a mole of air at STP.

Work out its internal energy from formula KE =Nk x2.5T

N = Avogadro’s Numberk = Boltzmann’s ConstantT =Standard Temperature in Kelvin units = 273KNow do the same at a height of one Kilometre with the same formula but with T2 = T -9.8The 9.8 comes from the drop in temperature due to adiabatic lapse rate drop for one kilometre

Subtract this value of internal energy from the STP value.

Now if you are correct this value will be equal to the gravitational potential energy gained.

PE = mghm = mass of one mole of air in kilogramsg = 9.81h = 1000All with the correct units implied

I think you will find that the energies will not equal one another.

To get the correct answer you need the barometric formulas for an adiabatic atmospheric expansion.Page 8 of this linkhttp://arxiv.org/pdf/1003.1508.pdf

Your theory does not give realistic answers.Try and work them out for yourselfcheck your answers against mine

Internal Energy lost = 203J

Potential Energy at 1000m = 284.2J

Work done in adiabatic expansion using the barometric formula’s = 203J

The parcel on returning to the Earth surface would gain 203JThat why your method (although quite plausible) does not work

Not one Joule of lost internal energy turns into gravitational potential energy

Bryan, please provide the equation/values you are using as code, eg in a format for Excel, so I can see exactly where things differ. All of my numeric solutions have agreed with many other published examples of the barometric equation solutions, many examples in this round-up of related posts that I just posted:

As to G&T, they were the original inspiration for the derivation and I used the same derivation of their formula #61 of their paper "On the Barometric Formulas And Their Derivation From Hydrodynamics and Thermodynamics"

I added the atmospheric center of mass concept, which is original as far as I know, to calculate ERL height where T = Te with the Sun, which was then substituted into G&T's equation #61 for z, and then added the solar forcing to determine the entire tropospheric temperature profile.

Work done = 204Joules which is the same as the value of lost internal energy given above.The value given as 203J should be 204J as I rounded off too early.

So not one Joule of internal energy lost is changed to Gravitational PE

You might then wonder where the 284.2J GPE above comes from?We must remember that for the rising parcel there must simultaneously be a falling parcel to fill the void left behind.The falling parcel loses 284.2J is reaching the surface.

So the first law is satisfied in all respects

Maxwell speculated that winds mixed the atmosphere.

The parcel is subject to two processes; the tendency to hydrostatic equilibrium and the attempt to reach thermodynamic equilibriumHydrostatic equilibrium is much faster than thermodynamic equilibriumHot air rises as cold air falls.

Ms, I must thank you once again for an outstanding number of posts particularly this year.

Many years ago, when taking my first course in microelectronics, we learned how to design op amp circuits assuming a "virtual ground" at the input terminal. The formula worked just as well if you connected the (-) terminal to ground as the (+) terminal so, I asked the professor, why couldn't we do that, and create a non-inverting amplifier? That brought quite a hearty chuckle and reddened my ears, I can tell you. The reason, of course, is that produces positive feedback, and your amplifier would do nothing but sit there and shriek. The formulas were just an approximation which worked under specific conditions, not iron clad laws for the device.

You have used some very top level formulas here. Formulas which hold under particular conditions. Specific heat, for example, is not at all constant over pressure and temperature. Nor do purely adiabatic processes actually exist. If you actually tried to get a lapse rate without any radiating gases in the atmosphere, your atmosphere would collapse to a densely packed, isothermal spherical shell consistent with the temperature from the SB relationship. The very title of this post is mondo cringeworthy. Continuous work from gravity? As likely as the Moon being made of green cheese, i.e., not even remotely within the realm of possibility. You might as well light up a neon sign blaring "I know nothing of physics", and start devoting your blog to perpetual motion machines.

You are overgeneralizing the relationships, and embarrassing yourself and others who, for other info, consider this blog first rate. I really wish you would get someone competent in the subject matter to review these things with you. Unfortunately, you appear to have latched on to a few like-minded, semi-trained folk who also rush in where angels fear to tread, and their external validation has given you untoward confidence in your conclusions. It is the bane of the internet era. Just stop, OK? Before you are completely relegated to the fringe, and I can no longer link to this blog in any serious argument.

"You have used some very top level formulas here. Formulas which hold under particular conditions. Specific heat, for example, is not at all constant over pressure and temperature."

True, but for > 99.9% of the atmosphere N2, O2, and Ar, the changes in specific heat are negligible over the range of temperatures in the atmosphere. CO2 at 0.04% has a negligible effect on the total, but CO2 does significantly change Cp/Cv with temperature, so that is something to consider for Venus and Mars, but not Earth.

"Nor do purely adiabatic processes actually exist."

They are pure enough to make the assumptions in the basic theory/equations above, which have been around for over a century. All of the above slides are from a series of lectures on thermodynamics and very well established physics/meteorology:

and found in hundreds of textbooks and other sources. There's nothing new here about well established adiabatic processes, Poisson relation and the heat capacity ratio Cp/Cv used by Maxwell to describe the atmospheric temperature gradient/greenhouse effect entirely without GHG radiative forcing. If the greatest physicist in history on the topic of radiation thought pressure creates the "GHE," shouldn't you?, or otherwise show your work on why you think Maxwell was wrong.

"If you actually tried to get a lapse rate without any radiating gases in the atmosphere, your atmosphere would collapse to a densely packed, isothermal spherical shell consistent with the temperature from the SB relationship."

False - I already calculated a Boltzmann distribution for a pure N2 atmosphere, which has a slightly higher center of mass and thus higher surface T, once again without GHGs link #3 here:

You don't think solar RF could inflate a pure N2 atmosphere? I show why that's nonsense at the equilibrium temperature of solar forcing.

"Continuous work from gravity? As likely as the Moon being made of green cheese, i.e., not even remotely within the realm of possibility."

Please read up on Newton's 2nd law of motion: F = ma = mg for the atmosphere, and is part of the derivation of all of the barometric formula including the lapse rate = -g/Cp. See the g in there? That's gravitational acceleration, a force doing Work on the atmosphere expanding/compressing gas packets/parcels ad infinitum, as show in the first slide above from a basic thermo lecture.

So, whoever you are anon, the burden of proof is now upon you to show the mathematics overturning the basic barometric equations well-known since the 1800's Maxwell's with book Theory of Heat. Handwaving doesn't count in my book.

Please read up on conservative forces. Gravity is a conservative force. It does no net work. This has been known for centuries. It is non-negotiable, and you are relegating yourself to the kook fringe.

"In this atmosphere, in its current state. This is circular reasoning. You have assumed the state of the system, then used that assumed state to show that your calculations lead to the assumed state."

Well sure, we are talking about Earth's atmosphere with all of the exact molecular constituents, molar masses, % of each in our of atmosphere, individual specific heats at constant pressure and volume, etc known to great precision at each level of the atmosphere all the way to space, and which on global average don't change. From this information in each atmospheric level, and knowledge of the geopotential height at every altitude, the temperature can be calculated on a global annual average and multi-decadal average at every single geopotential height of gravitational PE from the surface to 80,000km.

This has been done by hundreds of rocket scientists working at or under contract for the US Air Force, NOAA, and NASA, as well as other international space agencies, aviation applications, rocket applications, WMO, etc. duplicated multiple times over the past 50 years, without ever once using any radiative forcing from any GHGs whatsoever!

I have a post coming out later today demonstrating how to calculate the annual average complete atmospheric temperature profile at each altitude from 0-80,000 meters just based on calculating geopotential height (i.e. gravitational PE) and knowledge of the molecular constituents and the exact same barometric formulae in this post.

"Please read up on conservative forces. Gravity is a conservative force. It does no net work. This has been known for centuries. It is non-negotiable, and you are relegating yourself to the kook fringe."

In the first law

dU = 0 = Q - W

Basically what you are claiming is that in that equation W = 0, which is false, and disproven by the lecture slides I've provided above, as well as hundreds of thousands of other sources saying the same thing, as well as the derivations of how geopotential height (PE) and molecular thermodynamic properties alone determine the annual average temperature at every altitude from 0-80,000 meters, NOT greenhouse gas radiative forcing.

You aren't getting it. We are talking about the Earth in its present state. It's like the op amp problem. If I start out assuming the circuit is stable, then I can connect whichever lead I want to ground. But, that does not mean it will work, because I cannot take stability for granted.

Similarly, you cannot take for granted that you would be in the same state, having the same specific heats and so forth, if you had a different mechanism governing the atmosphere's thermal processes. The specific heat of air changes with temperature and pressure. The ideal gas law, used in your formulas, is not accurate for low temperatures and high pressures, or for non-homogeneous gas mixtures. The closer you look, the more assumptions you will find that go into your equations, assumptions which are legitimate for common application, but not generally reliable for extension beyond that range.

Look, you know the equation is wrong at some level. The lapse rate is not -g/cp all the way up. It stops increasing at the top of the troposphere and starts declining. Why? And, what's to stop that inflection point from moving higher or lower?

This is how you can get an isothermal atmosphere. Your equation may say the lapse rate is a particular value, but you do not have any theoretical means to predict in what region it holds. It could be an infinitesimal height, and what comes after that height is not addressed by your formulas.

If you want to know the full story, or at least a much more complete one, I urge you to consult a book by someone you should trust. This one:

Chapter 2 derives your formulas. Other chapters discuss how the result gets modified by other processes. Chapter 8, in particular, discusses the radiative physics which influence the lapse rate. It's heavy duty stuff, and should put to rest your concern that the climate science community has made an elementary mistake in these matters.

I'm well aware that just about every climatologist subscribes to the radiative greenhouse model, and I'm extremely familiar with what it claims and why those claims violate multiple physical laws, for which I have hundreds of posts, including papers in the literature admitting the rGHE violates both the 1st and 2nd law.

I just posted overwhelming physical and observational evidence, confirmed by work done by hundreds of physicists, atmospheric scientists, meteorologists for NASA, NOAA, USAF, etc that provides overwhelming physical and observational evidence that gravitational geopotential, a function of mass/gravity/altitude, not GHG RF, controls the lapse rate temperature profiles all the way to space. What more proof do you need that a paradigm shift back to the 1950's space program and Maxwell in 1872 that the gravito-thermal theory is the only one of the two GHE theories that can be correct?

Ironic isn't it how skeptics are called "gravity deniers" by some, but we're showing the "GHE" is from gravity, and thus the opposite true.

Also incredible how the most fundamental basic physics of gravity, pressure, mass, acceleration, 1st & 2nd laws of thermo, convection, that have formed the basis of actual physics for 2 centuries are all thrown in the trash since they're so inconvenient to AGW.

Basically Anonymous is claiming that if I have a balloon and inflate it with pure 100.000000000% Helium, or pure N2, Ar, O2, or any other non-IR active gas, that the balloon cannot inflate and will collapse due to the absence of greenhouse gases. Furthermore, he is claiming that if I release my Helium balloon (that he claims cannot inflate) and it rises in the atmosphere, the Helium balloon won't rise adiabatically, expand, and cool, since adiabatic processes don't occur in the atmosphere.

Astonishing. The trillion-dollar CAGW scam overturned by doing an experiment costing one dime, inflating a He balloon, releasing it, and seeing what happens. LOL

"There is no way that an atmosphere of O2 or N2 would fail to convect and produce a lapse rate because KE converts to PE with height."

Nonsense. Atmospheric particles are not in free flight. In fact, their mean velocities are much too small to maintain orbit on their own. They attain their height by being bouyed up by the particles below. There is no significant relationship between KE and PE until you get all the way up to the thermosphere.

"Basically Anonymous is claiming that if I have a balloon and inflate it with pure 100.000000000% Helium, or pure N2, Ar, O2, or any other non-IR active gas, that the balloon cannot inflate and will collapse due to the absence of greenhouse gases."

That's pretty silly. What does it have to do with gravity, anyway?

"Furthermore, he is claiming that if I release my Helium balloon (that he claims cannot inflate) and it rises in the atmosphere, the Helium balloon won't rise adiabatically, expand, and cool, since adiabatic processes don't occur in the atmosphere."

No, I am claiming it won't come back down again. At least, not until it pops, and then just the skin.

"What does the Work that lifts the Helium balloon from the surface to higher altitude?"

The work is done by whatever mechanism brought the helium to ground level in the first place, or whatever process liberated it from other ground level compounds, which may themselves have been previously deposited or produced by work from various sources. Just like the motion induced by the action of an ideal spring is sourced from the work used to extend or compress that spring. The spring, itself, does not spontaneously produce motion.

"I have a hot air balloon and turn on the burners at the surface for 20 minutes and then turn them off for good. What happens?"

No. Springs are a completely different issue that have zero to do with mass/gravity/pressure

The burners produce the kinetic heat energy (Q) which by the 1st Law

dU = 0 = Q - W

must be offset by an equal and opposite amount of Work (W) done by the force of gravity in pulling the balloon back to Earth while it is rising against gravity and thus accumulating gravitational potential energy (PE) and then pulling it back to Earth as the balloon cools.

Kinetic heat energy (Q) cannot both remain kinetic heat energy (Q) and still do work (W) without violating conservation of energy

Q = -W

notice the negative sign in front of W, which means the Work vector in the case of the hot air balloon pointing down from gravity has to be in the equal and opposite direction of the heat vector pointing up from convection or adiabatic expansion. The heat vector Q obviously cannot point both up and down at the same time to balance the 1st law equation.

Ideal spring action is the epitome of a conservative force. Gravity is a conservative force. It has everything to do with it.

Your example with the burners takes no account of the bouyancy. Clearly, the change in potential energy is not going to equal the heat put in - the ambient temperature is going to influence how high your balloon goes.

These little mental exercises can become very complicated and very convoluted, when you start peeling the layers of the onion. This approach isn't going to work, so I give up. Get the book by Salby I recommended and study the pertinent sections. I don't think I can make any more headway here.

If I use a forklift to lift my 10,000 kg deflated hot air balloon against the -9.8m/s/s gravitational acceleration vertical downward vector (instead of using the mass/pressure/density gradient as does the hot air balloon) up to 100 meters, and then lower the forklift down to the surface, according to you the forklift has done no Work since the balloon is right back in the same place it started, and allegedly energy has been "conserved," and the deflated balloon/forklift tip never accumulated any gravitational PE on the way up, right?

If the "conservative force" gravity has nothing to do with calculating the ~7 transitions in linear lapse rates = -g/Cp based upon geopotential heights and Cp in the various atmospheric layers from the surface to the edge of space, then why the heck do they use (g) to calculate the temperature and various lapse rates (of which dT/dh is a function, and not the cause) from the surface to edge of space?

See new post coming up right now definitively proving you are incorrect and the mass/pressure/gravity "GHE" perfectly explains the temperatures from the surface to every geopotential altitude 0-80,000+ meters.

If you still disagree, please show your work as I have, since a lot of handwaving and false proclamations about gravity cannot overturn Newton, Maxwell, and hundreds of atmospheric scientists that have produced the versions of the US Standard Atmosphere (and multiple other International Standard Atmospheres). These same models based entirely upon temperature as a function of geopotential height/mass/gravity/pressure are in widespread use today, not only for Earth, but are being used to model other thick planetary atmospheres as well. So, be prepared for a lot of work you're going to have to do to overturn the gravito-thermal "GHE" theory.

"I don't think I can make any more headway here."

Perhaps if you show your math and work, as I have, and thousands of other scientists have of the exact same principles, including in the lecture slides above, including thousands of other sources that say the exact same adiabatic equations and barometric equations which must include gravity, then and only then will you get any more headway here.

if as you say gravity is "conservative force" that can be ignored at the surface and any unit of atmospheres of Pressure at a given geopotential height of gravitational potential energy (PE) available to do Work (W)

Stephen Wilde wrote: "The net outcome is that the surface temperature of 288K is provided by 255K from the sun plus 33K from descending air but the surface cannot use that 33K for radiation to space because it is recycled into further convective uplift. Nevertheless the surface temperature will still be enhanced by 33K because the energy required by the ongoing convective cycle is still held at the surface."

Since radiative emission from the surface is entirely dependent on surface temperature, and pays absolutely no attention to any other process which is also removing energy from the surface (no traffic cop performs selection, after all), how do you arrive at "the surface cannot use that 33K for radiation to space". A joule is a joule, Stephen.